Is photon frequency intrinsic or observer-dependent?

[Roberto Pavani]

TL;DR

If frequency is just a projection $\nu = k^\mu u_\mu$, what distinguishes a radio photon from a gamma ray intrinsically?

In GR, the frequency of a photon is observer-dependent: $\nu = g_{\mu\nu} k^\mu u^\nu$, where $k^\mu$ is the photon 4-momentum and $u^\nu$ is the observer's 4-velocity.
Two observers in relative motion measure different frequencies from the same photon (gravitational/cosmological redshift, Doppler).
This means that "the frequency" is not (or not only) a property of the photon itself, but of the photon–observer pair.
My question: if we take this seriously, does it imply that all photons are in some sense "the same object" (null geodesics with $k^\mu k_\mu = 0$), and the only thing that distinguishes them observationally is the projection onto the observer's frame?
If so, what distinguishes a radio photon from a gamma ray photon intrinsically, as opposed to relationally?

 

[loop quantum gravity]

what's the definition of $k^\mu$ here? is it momentum up to constant hbar or something else? maybe a wave number?

 

[Matterwave]

Not sure why you bring GR into this and not sure why you bring photons into this.

The measured frequency of waves depend on relative motion of the emitter and the observer. This is just as true for light as it is for sound waves. You get a doppler effect for either.

all photons are in some sense "the same object" (null geodesics with $k^\mu k_\mu = 0$), and the only thing that distinguishes them observationally is the projection onto the observer's frame?

Another property that comes to mind is the photon's helicity. You're gonna have to clarify what you mean by "the same object". Do you just mean indistinguishability? I.e. that we can't apply Maxwell-Boltzmann statistics to photons?

If so, what distinguishes a radio photon from a gamma ray photon intrinsically, as opposed to relationally?

Nothing. The photon's frequency scales linearly to its energy $E=h\nu$ and energy is clearly frame dependent.

If you move very fast relative to the CMB for example, you'll see the CMB blue shifted in front of you and red shifted behind you. And in fact, we can use this to detect our motion through the CMB (we call this the "Solar Dipole").

See the multipole section of: https://en.wikipedia.org/wiki/Cosmic_microwave_background?hl=en-US

 

[Matterwave]

Just to give a 1-sentence answer: the frequency of light is observer dependent.

 

[Dale]

what distinguishes a radio photon from a gamma ray photon intrinsically, as opposed to relationally?

Nothing.

 

[Roberto Pavani]

Thanks for the replies. A follow-up: if frequency is observer-dependent, and $E = h\nu$, then the photon's energy is also observer-dependent.
Does this mean a photon doesn't "have" an energy in any intrinsic sense, only in relation to an observer?

 

[Sagittarius A-Star]

Thanks for the replies. A follow-up: if frequency is observer-dependent, and $E = h\nu$, then the photon's energy is also observer-dependent.
Does this mean a photon doesn't "have" an energy in any intrinsic sense, only in relation to an observer?

Yes, because it is massless.